Math 591  General
and Differential Topology  Fall 2001

Time and Place:
MWF 1011 pm in EH 2866

Instructor: Ralf Spatzier,
5848 East Hall, 7632192, spatzier@math.lsa.umich.edu

Office Hours: Fr
11 am and 2 pm or by appointment

Text: required:
``Topology" by Munkres, 2nd edition, Prentice Hall
optional:
``Differential Topology'', Guillemin/Pollack, Prentice Hall
Prerequisites:
Familiarity with undergraduate analysis is recommended
Course Outline: This
course is an introduction to point set and differential topology. Specifically,
we will introduce abstract topological spaces and their basic properties.
Then we will discuss the properties of connectedness and compactness. We
will construct new topological spaces from old ones, such as subspaces,
products and quotients, group actions and orbit spaces. Finally, we will
introduce manifolds and differential topology, in particular tangent spaces,
the regular value theorem, Whitney's embedding theorem and transversality.
Students with a strong background in pointset and differential topology
may want to consider taking Math 537 instead. Math 591 will cover the prerequisites
for the portions of the topology QR which concern point set topology and
differential topology.
Problem Session: TBA
Grading Policy: homework
40%; midterm 30%; final exam 30%;
Homework Policy: Homework
will be assigned weekly and collected on Friday. You may discuss the homework
problems with other students, but you should write up the solutions on
your own.
Homeworks :You can download
the homework assignments below as postscript or pdf (Adobe Acrobat) files:
